Solving a Pulley System: Friction, Tension & Acceleration

[bungie77]

Homework Statement

http://img214.imageshack.us/img214/6531/pulleysystemph6.th.jpg

Homework Equations

sum of forces

The Attempt at a Solution

So I tried summing the forces in the x-direction where

m*a (block a) = -Ff + T = m(block a)*g*u + m*a(block b) + m*g(block b)

where u is the coefficient of friction, T is the tension in the rope and Ff is the frictional force.

I'm not, however, getting an answer on the multi choice list. Is there something I'm missing?

 

[bungie77]

*this is the link to the picture in case the thumbnail doesn't work

http://img214.imageshack.us/my.php?image=pulleysystemph6.jpg

 

[PhanthomJay]

You've got to look at each block separately when doing these problems. This is essential. Draw a free body diagram for each. Identify the forces acting on each block and use Newton 2. You'll have 2 equations with 2 unknowns that you can solve. Note that the magnitudes of the tension and acceleration for each block are the same.

 

[bungie77]

well I've been doing that but i can't seem to get the right answer... i was wondering if maybe i was screwing something up with the directions...

so far I've come to the following;

for block A;

Fx = T - Uk*N = mA*ax
Fy = N - mA*g = 0

So essentially, Fx = T - Uk*mA*g = mA*ax

For block C;

Fy = T - mC*g = mC*ay

I understand ay = ax but i can't seem to get the right answer... I'm getting something around 1.6 :(

 

[PhanthomJay]

well I've been doing that but i can't seem to get the right answer... i was wondering if maybe i was screwing something up with the directions...

so far I've come to the following;

for block A;

Fx = T - Uk*N = mA*ax
Fy = N - mA*g = 0

So essentially, Fx = T - Uk*mA*g = mA*ax

For block C;

Fy = T - mC*g = mC*ay

I understand ay = ax but i can't seem to get the right answer... I'm getting something around 1.6 :(

Oh, good, you are on track; only error you made was for block C, since it accelerates down, its weight must be greater than T, so your plus/minus signs are incorrect. It should be mCg - T = mC*ay. Do you see why?

 

[bungie77]

ahhh yeah of course. and since the tension is obviously greater in block A the signs are opposite to block C. thanks :)